We consider different patterns of infinite technological adoption choices b
y firms in a Bertrand duopoly. Every period technological progress provides
a sequence of cost reducing innovations. The equilibrium concept is Markov
perfect equilibrium. We analyze conditions for which equilibrium adoption
leads to persistent leadership and those where firms alternate in adoption
inducing leapfrogging. Only leapfrogging leads to technological improvement
in the long run. Demand conditions play a crucial role in determining whet
her leapfrogging can be perpetual in Bertrand duopoly.